# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0260
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0260?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 129v, page id 00068200:0260
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=260
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000260.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 94 lines, status machine
# Lines: 94 recognised, mean confidence 0.79
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

sb
2ab
ne ioventa junu
anferatur tum factu ex duobus numeras non quadritisategris.
C= X+
et X4 d7 fiet e
X F DX, + cd ex
+c
V
ergo  7 cd, et d, a, ilem D  naC SI ergo a=  a +C
s
unde sequitur CH Hac nc a pi et vel a A e. ergo dejoc pya.
Sed si aurmeri essent in aqualas. i A+ C, et X. +cF d. 1. fie multi
plicando:
~
+ ee X +c
tnc
 et habebimus a  + cd
Ead
1
a
74. Cum Domini a Osannam i_ et d   = ME. item id 1 a ∞ E ergos iac - c 54- 
Paulo aute communicationem suarum
artium mihi negasset
fiet ergo a H c. Ergo d 0 equare alia ad rem istam consequen
y + c + d, sive y + 2c Y + c
+ d
Ergo  2c + d  2b + 2a. sive d 1 2b + 2 a = 2C. Item d B
+ cd
62 29b + a - c
Ergo 2bc+ 2 ac  fc YI eb +2ab + a -  sumendoque a F1 1, fiet:
2bc + 2C 2bc - c - b  X +a + 2ba = _ 2 ca ergo + b +C FI a + 2b - 2c4
Quae summa ita formanda est, ut inde extrahi queat Radix debetero a, esse quadratus  sive fiet
+ bl+ ce, 2b a e s et
et
0
dam methodo opus est, nimorum tentenus pontre y b F, X. Junque
y + c
Quarendus ergo tantum
duorum
est numerus quadratus, compositus ex alio quadrato, et duplicata differentia quorum libet aliorum
numerorum. Ideo loco et, ponamue X + n 2fX + f
conferenda cum X + cgX
fiet
Ergo conferendum cum X + 2h X + h
Ergo h H +f + fl sive 
Ergo h
V
ergo
v
s
2l + b
f~ + 2fl + d.. Ergo f +2fl+
2
vel
+ 2
+2gl -
2
il
et pro b, ponemus X + g.
Unumque ex numeris ponemus X + g,
aeterum R, fiet 2bXl + 2gC
es - 2cl
I f + 2gl, - 2cl
2fl + l 5 29l - 2cl sive 2f + l ( 29 - 2c. sue fr 29 - 2c - l
ergo e 1 4g X
et +2bl = 2cl, dabunt
2xt +2gl- 2cl
 4 2
+ 29 - 2c - l X + 497 + 8gc - 4gl + 4c + 4cl + 12 2
ex qua quantitate extrahi radix potest, et quia h B f + l, eris et
h radix quantitatis propositae, et habebimus: +bl+ et
+qx) fagl +4cl
YX + 29 - 2C - l
s
+. 29l
c
7
2
X
9- 2c = l erit radix X +79 + 2c . l +
2X F29 - 3c- sl 2.g .c. t sive xl Agl + Ac lsi agX 4eX Elx+
et e erit X seu X + f, erit X + 29 - 26 -l resumendoque aequationem
C, fiet +4Xl + agl facl ( et sive 4X
12 10
++X + AgX. AcX 3X jamque ponendo 4X +49 -69l+ +C (7 0. sive fX (+) g(+ s)C
batebimus: + (4) gl f (+) 4 cl + 4cl
pro X ponatur Z + m. et ZN (+(9) (+)c sublatis
qu fiet 4Z2 +49- 89c + 4c5 p7 0, omittentur ergo sed ex locis ubi g, vel ex in xdrcuntur orientur quodrata nova, fiet
et loco CX nmp 1t termim examinandi loco 4X + 12gX + 4g = BgC + 4c, habebimus 4m (4) +mg (+) +C (+ )12 gH (+) 12Cg, ubi
et rusus quoedam comescanti purenus es n + _. fet Fncg er Zugn F ang. cstietrem 4)amnspin celi. Sed ita incidumu
t 2
e
pro X substituatur Y + h, fiel